Follow-up signals from superradiant instabilities of black hole merger remnants

Superradiant instabilities can trigger the formation of bosonic clouds around rotating black holes. If the bosonic field growth is sufficiently fast, these clouds could form shortly after a binary black hole merger. Such clouds are continuous sources of gravitational waves whose detection (or lack thereof) can probe the existence of ultralight bosons (such as axionlike particles) and their properties. Motivated by the binary black hole mergers seen by Advanced LIGO so far, we investigate in detail the parameter space that can be probed with continuous gravitational wave signals from ultralight scalar field clouds around black hole merger remnants with particular focus on future ground-based detectors (A+, Voyager and Cosmic Explorer). We also study the impact that the confusion noise from a putative stochastic gravitational-wave background from unresolved sources would have on such searches and we estimate, under different astrophysical priors, the number of binary black hole merger events that could lead to an observable postmerger signal. Under our most optimistic assumptions, Cosmic Explorer could detect dozens of postmerger signals.

Figure 1

The value of $M\mu$ (left $y$-axis) maximizing the superradiant instability timescale $1/(M{\omega }_I)$ (right $y$-axis) of the dominant scalar field mode ($\ell =m=1$) as a function of the dimensionless BH spin $\chi$. The superradiant instability timescale on the right $y$-axis is in natural units. To convert it to seconds, it should be multiplied by $GM/c^3$ (for quick estimates, note that $G{M}_{\odot }/c^3\approx 5\times {10}^{-6}\mathrm{s}$).

Figure 2

Instability timescale for a remnant BH of mass $63M_{\odot }$ (the GW150914 remnant mass) and selected values of the remnant BH spins. The timescale (in years) is plotted as a function of both the GW frequency (bottom $x$-axis) and of the boson mass in eV (top $x$-axis).

Figure 3

Relative intrinsic amplitude above the 95%-confidence strain upper limit at AdLIGO, A+, Voyager and Cosmic Explorer for GW signals from BHs with spin $\chi =0.7$ at redshift $z=0.1$ and detector-frame mass in the range $[10,1000]M_{\odot }$. We choose the boson mass such that $M\mu$ maximizes the intrinsic amplitude, and we compute $h_0^{95\%}$ using a coherent observation time $T_{\mathrm{coh}}=10$ days and a number of segments such that the total observation time is 2 years.

Figure 4

Contour plot in the $(M,m_s)$ plane (where $M$ is the detector-frame BH mass) of BH/cloud signals at $z=0.1$ that would be detectable by Cosmic Explorer. We consider a semicoherent search with $T_{\mathrm{coh}}=10$ days and different observation times (indicated by the different colors) with (dashed) and without (solid) self-confusion noise. Our estimate of the self-confusion noise is described in the main text. For all plots we consider superradiant instabilities that grow within 30 days. The four panels correspond to different BH spins $\chi$, as indicated in the legend.

Figure 5

Same as Fig. 4 for a system with BH spin $\chi =0.8$ detected at smaller redshift ($z=0.05$).

Figure 6

Stochastic background fluxes (in color) plotted over the noise PSD (in black) for the different detectors.

Figure 7

Merger events that could have detectable postmerger GW signals without (left panel) and with (right panel) self-confusion noise for Cosmic Explorer, assuming $T_{\mathrm{coh}}=10$ days and one year of continuous observation time. The different curves correspond to different astrophysical assumptions on the progenitor masses and spins, as described in the main text. The dashed black line marks the threshold to have at least one observable event within one year of observation.

Figure 8

Left panel: GW intrinsic amplitude $h_0^{(\tilde{\ell })}r/M$ [c.f. Eq. (12)] for the $\tilde{\ell }=2$ (solid lines) and $\tilde{\ell }=3$ (dashed lines) modes as a function of $M\mu$ and different selected values of the BH spin ($\chi =0.7$, 0.9, 0.99). Right panel: GW intrinsic amplitude for the $\tilde{\ell }=2$ and $\tilde{\ell }=3$ modes computed at the value of $M\mu$ that maximizes the superradiant instability growth rate (cf. Fig. 1).